Welcome to Open Science
Contact Us
Home Books Journals Submission Open Science Join Us News
The Alternating Projection Algorithm for the Symmetric Arrowhead Solution of Matrix Equation A×B=C
Current Issue
Volume 4, 2016
Issue 4 (August)
Pages: 23-27   |   Vol. 4, No. 4, August 2016   |   Follow on         
Paper in PDF Downloads: 45   Since Mar. 29, 2017 Views: 1200   Since Mar. 29, 2017
Minghui Wang, Department of Mathematics, Qingdao University of Science & Technology, Qingdao, China.
Luping Xu, Department of Mathematics, Qingdao University of Science & Technology, Qingdao, China.
Juntao Zhang Zhang, Department of Mathematics, Qingdao University of Science & Technology, Qingdao, China.
Based on the alternating projection (AP) algorithm, the constrained matrix equation A×B=C and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.
Iterative Method, Symmetric Arrowhead Matrix, The Alternating Projection Algorithm
Y. F. Xu, An inverse eig-envalue problem for a special kind of matrices. Math. Appl., 1 (1996) 68-75.
C. J. Meng, X. Y. Hu, L. Zhang, The skew symmetric orthogonal solution of the matrix equation AX=B, Linear Algebra Appl. 402 (2005) 303-318.
Li Jiaofen, Zhang Xiaoning, Peng Zhenyun, Alternative projection algorithm for single variable linear constraints matrix equation problems, Mathematica Numerical Since, 36 (2014) 143-162.
Y. X. Peng, X. Y. Hu, L. Zhang, An interation method for the symmetric solutions and the optimal approximation solution of the matrix equation AXB = C, Applied Mathematics and Computation, 160 (2005) 763-777.
Z. Y. Peng, A matrix LSQR iterative method to solve matrix equation AXB = C, International Journal of Computer Mathematics, 87 (2010) 1820-1830.
J. F. Li, X. F. Duan, L. Zhang, Numerical solutions of AXB = C for mirror symmetric matrix X under a specified submatrix constraint. Computing, 90 (2010) 39-56.
Von Neumann J., Functional Operators. II. The Geometry of Spaces, Annals of Mathematics Studies, vol.22, Princeton University Press, Princeton, 1950.
Cheney W., Goldstein A. Proximity maps for convex sets, Proceedings of the American Mathematical Society, 10 (1959) 448-450.
Hongyi Li, Zongsheng Gao, Di Zhao. Least squares solutions of the matrix equation with the least norm for symmetric arrowhead matrices. Appl. Math. Comput., 226(2014) 719-724.
Y. F. Xu. An inverse eigenvalue problem for a special kind of matrices. Math. Appl., 1(1996)68-75.
G. P. Xu, M. S. Wei, D. S. Zhang, On solutions of matrix equations AXB +CYD=E. Linear Algebra Appl., 279 (1998) 93-109.
A. P. Liao, Z. Z. Bai, Y. Lei, Best approximate solution of matrix equation AXB +CYD=E. SIAM J. Matrix Anal. Appl., 27(2006) 675-688.
Lin T Q. Implicitly restarted global FOM and GMRES for nonsymmetric matrix equations and Sylvester equations[J]. Appl. Math. Comput., 167 (2005) 1004-1025.
Shifang Yuan, Qingwen Wang and Xuefeng Duan, On solutions of the quaternion matrix equation AX=B and their application in color image restoration [J], Appl. Math. Comput., 221 (2013) 10-20.
Yuming Feng, Chuandong Li, Tingwen Huang. Sandwich control systems with impulse time windows [J]. International Journal of Machine Learning and Cybernetics. (2016) 1-7.
Yuming Feng, Chuandong Li, Tingwen Huang. Periodically multiple state-jumps impulsive control systems with impulse time windows, Neurocomputing 193 (2016) 7–13.
Huamin Wang, Shukai Duan, Chuandong Li, Lidan Wang, Tingwen Huang. Linear impulsive control system with impulse time windows, Journal of Vibration and Control, 14 (2016) 1-8.
Open Science Scholarly Journals
Open Science is a peer-reviewed platform, the journals of which cover a wide range of academic disciplines and serve the world's research and scholarly communities. Upon acceptance, Open Science Journals will be immediately and permanently free for everyone to read and download.
Office Address:
228 Park Ave., S#45956, New York, NY 10003
Phone: +(001)(347)535 0661
Copyright © 2013-, Open Science Publishers - All Rights Reserved